During 'The Anarchy' of the war between Stephen and Matilda over the throne of England, David I of Scotland took advantage of English weakness to seize the lands of Northumbria, directly south of the Scottish border. Stephen was forced to recognise Northumbria as Scottish territory. However, it did not remain Scottish for long: it was won back by Henry II less than ten years later, in 1157.
Editors. "Northumbria ceded to David I of Scotland". The Literary Encyclopedia. First published 31 July 2012
[http://www.litencyc.com/php/stopics.php?rec=true&UID=1956, accessed 02 September 2014.]